Question

If the point (2, k) lies outside the circles

x² + y² + x – 2y – 14 = 0 and x² + y² = 13, then

• A. kĪ (–3, –2) $\cup$ (3, 4)
• B. kĪ (–3, 4)
• C. kĪ (–, –3) $\cup$ (4, )
• D. kĪ (–, –2) $\cup$ (3, )

Answer 1

Answer: (C)

kĪ (–, –3) $\cup$ (4, )

Answer 2

P(2, k)

S ŗ x² + y² + x – 2y – 14 = 0

S₁ > 0

Ž 4 + k² + 2 – 2k – 14 > 0

Ž k² – 2k – 8 > 0

Ž (k – 4) (k + 2) > 0

k < – 2, k > 4 . . . (1)

S₁ = x² + y² – 13 = 0

$S_{1}^{'}$ = 4 + k² – 13 > 0

Ž k² – 9 > 0

Ž (k – 3) (k + 3) > 0

k < – 3, k > 3 . . . . (2)

from (1) and (2)

Ž k Ī (–, –3) $\cup$ (4, )